Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and measurements of objects in space. It involves the analysis of points, lines, angles, planes, and solid figures, such as polygons, circles, spheres, and cones. Geometry is a fundamental subject in mathemat...
Geometry is a branch of mathematics that deals with the study of shapes, sizes, and positions
of objects in space. It is one of the oldest branches of mathematics, with its origins dating back
to ancient Greece. The word "Geometry" is derived from the Greek word’s "geo" meaning
"earth" and "metron" meaning "measure."
Basic Definitions
In Geometry, there are some basic definitions that you need to understand. These definitions provide a
foundation for the study of Geometry. Some of the important definitions are:
Point: A point is a position in space that has no length, width, or thickness. It is represented by a
dot.
Line: A line is a straight path that extends infinitely in both directions. It has no thickness and is
represented by a straight line with two arrows at the ends.
Ray: A ray is a part of a line that has one endpoint and extends infinitely in one direction. It is
represented by a straight line with one arrow at the end.
Line Segment: A line segment is a part of a line that has two endpoints. It is represented by a
straight line with two endpoints.
Angle: An angle is a figure formed by two rays that have a common endpoint. The common
endpoint is called the vertex of the angle.
Plane: A plane is a flat surface that extends infinitely in all directions.
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, Circle: A circle is a set of all points that are equidistant from a fixed point called the center of the
circle.
Formulas
Geometry involves a lot of formulas that are used to calculate the area, perimeter, volume, and other
properties of geometric shapes. Some of the important formulas are:
Area of a Triangle: The area of a triangle is given by the formula A = (1/2)bh, where b is the base
of the triangle and h is its height.
Perimeter of a Triangle: The perimeter of a triangle is the sum of the lengths of its three sides.
Area of a Circle: The area of a circle is given by the formula A = πr^2, where r is the radius of the
circle.
Circumference of a Circle: The circumference of a circle is given by the formula C = 2πr, where r
is the radius of the circle.
Volume of a Sphere: The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the
radius of the sphere.
Surface Area of a Cube: The surface area of a cube is given by the formula SA = 6s^2, where s is
the length of each side of the cube.
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